ECONOMICALLY OPTIMAL MARINE RESERVES WITHOUT SPATIAL HETEROGENEITY IN A SIMPLE TWO‐PATCH MODEL

Bioeconomic analyses of spatial fishery models have established that marine reserves can be economically optimal (i.e., maximize sustainable profit) when there is some type of spatial heterogeneity in the system. Analyses of spatially continuous models and models with more than two discrete patches have also demonstrated that marine reserves can be economically optimal even when the system is spatially homogeneous. In this note we analyze a spatially homogeneous two‐patch model and show that marine reserves can be economically optimal in this case as well. The model we study includes the possibility that fishing can damage habitat. In this model, marine reserves are necessary to maximize sustainable profit when dispersal between the patches is sufficiently high and habitat is especially vulnerable to damage.     

OPTIMAL CONTROL APPLIED TO RIFT VALLEY FEVER

Abstract Rift Valley Fever (RVF) virus is a mosquito‐born pathogen that infects livestock but it also has the capability to infect humans through direct or indirect contact with blood or organs of infected animals and by bites from infected mosquitos. The economic and social cost of the disease to rural populations can lead to a cascade of negative effects on the sustainability of animal and human populations. Vaccines exist to protect against this disease. Through a compartment model depicting the interactions leading to the spread of RVF in Aedes and Culex mosquitos and a livestock population, an optimal control problem is developed to minimize the number of vaccinated livestock at the final time while minimizing the negative effects of the infected Aedes and Culex mosquitos and the cost of the vaccination process. The unique optimal vaccination strategy is produced for given high transmission parameters and numerical results portray that vaccination depends on the level of effectiveness of the protocol.